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United States Patent Application 20170206490
Kind Code A1
Deshpande; Ajay A. ;   et al. July 20, 2017

SYSTEM AND METHOD TO DYNAMICALLY INTEGRATE COMPONENTS OF OMNI-CHANNEL ORDER FULFILMENT

Abstract

The methods, systems, and computer program products described herein provide optimized order fulfillment in an omni-channel order fulfillment system. In an aspect of the present disclosure, dimensional multipliers for a plurality of dimensions are optimized by iteratively solving a multi criteria decision analysis framework (MCDA) sequentially for each dimension. The optimized dimensional multipliers may be used by the MCDA as inputs along with current data to generate a solution for each dimension. The solution may be integrated by the order fulfillment system to optimize order fulfillment based on the current data.


Inventors: Deshpande; Ajay A.; (White Plains, NY) ; Gupta; Saurabh; (Irving, TX) ; Hampapur; Arun; (Norwalk, CT) ; Koc; Ali; (White Plains, NY) ; Li; Yingjie; (Chappaqua, NY) ; Liu; Xuan; (Yorktown Heights, NY) ; Milite; Christopher S.; (Oxford, CT) ; Quanz; Brian L.; (Yorktown Heights, NY) ; Tan; Chek Keong; (Danbury, CT) ; Xing; Dahai; (White Plains, NY) ; Zheng; Xiaobo; (Shanghai, CN)
Applicant:
Name City State Country Type

International Business Machines Corporation

Armonk

NY

US
Family ID: 1000001958466
Appl. No.: 15/153900
Filed: May 13, 2016


Related U.S. Patent Documents

Application NumberFiling DatePatent Number
62279738Jan 16, 2016

Current U.S. Class: 1/1
Current CPC Class: G06Q 10/087 20130101; G06F 3/0482 20130101; G06F 3/04847 20130101; G06Q 10/083 20130101
International Class: G06Q 10/08 20060101 G06Q010/08; G06F 3/0482 20060101 G06F003/0482; G06F 3/0484 20060101 G06F003/0484

Claims



1. A method, comprising: receiving, by at least one processor, historical data associated with an order fulfillment system; setting, by at least one processor, a dimensional multiplier for each of a plurality of dimensions of the order fulfillment system to an initial pre-determined value; iteratively performing the following until the dimensional multipliers for each of the plurality of dimensions have been optimized: running, by at least one processor, a multi criteria decision analysis framework based on the historical data and the dimensional multipliers for the plurality of dimensions to generate a solution value for each dimension; comparing, by at least one processor, the solution value for each dimension to an interval including a minimum and maximum solution value for each dimension; determining, by at least one processor, whether one or more of the dimensional multipliers need to be adjusted based at least in part on the comparison; if it is determined that one or more of the dimensional multipliers need to be adjusted: adjusting, by at least one processor, the one or more dimensional multipliers based at least in part on the comparison; and performing, by at least one processor, the next iteration based at least in part on the one or more adjusted dimensional multipliers; if it is determined that none of the dimensional multipliers need to be adjusted, determining that the dimensional multipliers for each of the plurality of dimensions have been optimized; receiving, by at least on processor, current data associated with a current state of the order fulfillment system; and running, by at least one processor, the multi criteria decision analysis framework based on the current data and the optimized dimensional multipliers for each of the plurality of dimensions to generate an optimized solution; and performing order fulfillment based on the optimized solution.

2. The method of claim 1, wherein determining whether one or more of the dimensional multipliers need to be adjusted based at least in part on the comparison includes receiving by the order fulfillment system an indication from a user device that one or more of the dimensional multipliers need to be adjusted.

3. The method of claim 1, wherein adjusting the one or more dimensional multipliers based at least in part on the comparison includes receiving from a user device an adjusted value of the one or more of the dimensional multipliers.

4. The method of claim 3, further comprising: causing the presentation of a graphical user interface on a display of the user device, the graphical user interface including one or more elements that are adjustable by a user of the user device, each element configured to adjust the value of one of the dimensional multipliers; receiving from the user device an indication that one or more of the elements has been adjusted; and adjusting the value of the corresponding one or more dimensional multipliers based on the received indication.

5. The method of claim 1, wherein the historical data comprises at least one of SKUs for at least one item, order fulfillment nodes, a subset of order fulfillment notes having items of a particular SKU, and shipping costs.

6. The method of claim 1, wherein the initial pre-determined value is set in advance by a user.

7. The method of claim 1, wherein at least one of the plurality of dimensions is selected from the group consisting of reducing backlog, avoiding markdowns, minimizing shipping costs, and minimizing labor costs.

8. A system, comprising: at least one processor programmed for: receiving, by at least one processor, historical data associated with an order fulfillment system; setting, by at least one processor, a dimensional multiplier for each of a plurality of dimensions of the order fulfillment system to an initial pre-determined value; iteratively performing the following until the dimensional multipliers for each of the plurality of dimensions have been optimized: running, by at least one processor, a multi criteria decision analysis framework based on the historical data and the dimensional multipliers for the plurality of dimensions to generate a solution value for each dimension; comparing, by at least one processor, the solution value for each dimension to an interval including a minimum and maximum solution value for each dimension; determining, by at least one processor, whether one or more of the dimensional multipliers need to be adjusted based at least in part on the comparison; if it is determined that one or more of the dimensional multipliers need to be adjusted: adjusting, by at least one processor, the one or more dimensional multipliers based at least in part on the comparison; and performing, by at least one processor, the next iteration based at least in part on the one or more adjusted dimensional multipliers; if it is determined that none of the dimensional multipliers need to be adjusted, determining that the dimensional multipliers for each of the plurality of dimensions have been optimized; receiving, by at least on processor, current data associated with a current state of the order fulfillment system; and running, by at least one processor, the multi criteria decision analysis framework based on the current data and the optimized dimensional multipliers for each of the plurality of dimensions to generate an optimized solution value for each dimension; and performing order fulfillment based on the optimized solution.

9. The system of claim 8, wherein determining whether one or more of the dimensional multipliers need to be adjusted based at least in part on the comparison includes receiving by the order fulfillment system an indication from a user device that one or more of the dimensional multipliers need to be adjusted.

10. The system of claim 8, wherein adjusting the one or more dimensional multipliers based at least in part on the comparison includes receiving from a user device an adjusted value of the one or more of the dimensional multipliers.

11. The system of claim 10, the at least one processor further programmed for: causing the presentation of a graphical user interface on a display of the user device, the graphical user interface including one or more elements that are adjustable by a user of the user device, each element configured to adjust the value of one of the dimensional multipliers; receiving from the user device an indication that one or more of the elements has been adjusted; and adjusting the value of the corresponding one or more dimensional multipliers based on the received indication.

12. The system of claim 8, wherein the historical data comprises at least one of SKUs for at least one item, order fulfillment nodes, a subset of order fulfillment notes having items of a particular SKU, and shipping costs.

13. The system of claim 8, wherein the initial pre-determined value is set in advance by a user.

14. The system of claim 8, wherein at least one of the plurality of dimensions is selected from the group consisting of reducing backlog, avoiding markdowns, minimizing shipping costs, and minimizing labor costs.

15. A computer program product storing instructions that, when executed by at least one processor, program the at least one processor for: receiving, by at least one processor, historical data associated with an order fulfillment system; setting, by at least one processor, a dimensional multiplier for each of a plurality of dimensions of the order fulfillment system to an initial pre-determined value; iteratively performing the following until the dimensional multipliers for each of the plurality of dimensions have been optimized: running, by at least one processor, a multi criteria decision analysis framework based on the historical data and the dimensional multipliers for the plurality of dimensions to generate a solution value for each dimension; comparing, by at least one processor, the solution value for each dimension to an interval including a minimum and maximum solution value for each dimension; determining, by at least one processor, whether one or more of the dimensional multipliers need to be adjusted based at least in part on the comparison; if it is determined that one or more of the dimensional multipliers need to be adjusted: adjusting, by at least one processor, the one or more dimensional multipliers based at least in part on the comparison; and performing, by at least one processor, the next iteration based at least in part on the one or more adjusted dimensional multipliers; if it is determined that none of the dimensional multipliers need to be adjusted, determining that the dimensional multipliers for each of the plurality of dimensions have been optimized; receiving, by at least on processor, current data associated with a current state of the order fulfillment system; and running, by at least one processor, the multi criteria decision analysis framework based on the current data and the optimized dimensional multipliers for each of the plurality of dimensions to generate an optimized solution value for each dimension; and performing order fulfillment based on the optimized solution.

16. The computer program product of claim 15, wherein determining whether one or more of the dimensional multipliers need to be adjusted based at least in part on the comparison includes receiving by the order fulfillment system an indication from a user device that one or more of the dimensional multipliers need to be adjusted.

17. The computer program product of claim 15, wherein adjusting the one or more dimensional multipliers based at least in part on the comparison includes receiving from a user device an adjusted value of the one or more of the dimensional multipliers.

18. The computer program product of claim 17, the instructions, when executed by the at least one processor, further programming the at least one processor for: causing the presentation of a graphical user interface on a display of the user device, the graphical user interface including one or more elements that are adjustable by a user of the user device, each element configured to adjust the value of one of the dimensional multipliers; receiving from the user device an indication that one or more of the elements has been adjusted; and adjusting the value of the corresponding one or more dimensional multipliers based on the received indication.

19. The computer program product of claim 15, wherein the historical data comprises at least one of SKUs for at least one item, order fulfillment nodes, a subset of order fulfillment notes having items of a particular SKU, and shipping costs.

20. The computer program product of claim 15, wherein at least one of the plurality of dimensions is selected from the group consisting of reducing backlog, avoiding markdowns, minimizing shipping costs, and minimizing labor costs.
Description



RELATED APPLICATION

[0001] This application claims the benefit of and priority to U.S. Provisional Application Ser. No. 62/279,738, filed Jan. 16, 2016, the entire contents of which are incorporated herein by reference.

FIELD

[0002] The present application relates generally to order fulfillment, and more particularly to optimizing an order fulfillment system.

BACKGROUND

[0003] Omni-channel retailing systems provide consumers with a seamless and unified purchasing experience via both offline and online sales channels. The consumers may view and purchase goods and/or services through a variety of different platforms including on-line e-commerce web portals, mobile applications, brick and mortar stores, catalogues, and other similar platforms. Orders placed by a consumer may be fulfilled either directly, for example, the consumer may purchase the item at the brick and mortar store, or through the use of a shipping company or postage carrier, for example, delivered to a location of the consumer's choosing.

BRIEF SUMMARY

[0004] The methods, systems, and computer program products described herein provide optimization for omni-channel order fulfillment systems. In an aspect of the present disclosure, dimensional multipliers for a plurality of dimensions are optimized by iteratively solving a multi criteria decision analysis framework (MCDA) sequentially for each dimension. The optimized dimensional multipliers may be used by the MCDA as inputs along with current data to generate a solution for each dimension. The solution may be integrated by the order fulfillment system to optimize order fulfillment based on the current data.

[0005] In an aspect of the present disclosure, a method is disclosed including receiving historical data associated with an order fulfillment system and setting a dimensional multiplier for each of a plurality of dimensions of the order fulfillment system to an initial pre-determined value. The method iteratively performs the following until the dimensional multipliers for each of the plurality of dimensions have been optimized: running a multi criteria decision analysis framework based on the historical data and the dimensional multipliers for the plurality of dimensions to generate a solution value for each dimension, comparing the solution value for each dimension to an interval including a minimum and maximum solution value for each dimension, determining whether one or more of the dimensional multipliers need to be adjusted based at least in part on the comparison, if it is determined that one or more of the dimensional multipliers need to be adjusted: adjusting the one or more dimensional multipliers based at least in part on the comparison, and performing the next iteration based at least in part on the one or more adjusted dimensional multipliers, if it is determined that none of the dimensional multipliers need to be adjusted, determining that the dimensional multipliers for each of the plurality of dimensions have been optimized. Once the dimensional multipliers have been optimized, the method further includes receiving current data associated with a current state of the order fulfillment system, running the multi criteria decision analysis framework based on the current data and the optimized dimensional multipliers for each of the plurality of dimensions to generate an optimized solution value for each dimension, and applying the optimized solution value to the order fulfillment system.

[0006] In aspects of the present disclosure apparatus, systems, and computer program products in accordance with the above aspect may also be provided.

[0007] Further features as well as the structure and operation of various embodiments are described in detail below with reference to the accompanying drawings. In the drawings, like reference numbers indicate identical or functionally similar elements.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

[0008] FIG. 1 illustrates a schematic of an example computer or processing system that may implement an order fulfillment system in accordance with an embodiment of the present disclosure.

[0009] FIG. 2 is a diagram of an optimization model illustrating components used for optimizing an order fulfillment plan in accordance with an embodiment of the present disclosure.

[0010] FIG. 3 illustrates an example of a user interface in accordance with an embodiment of the present disclosure.

[0011] FIG. 4 is a flow chart illustrating a method of optimizing an order fulfillment system according to an embodiment of the present disclosure.

[0012] FIG. 5 depicts a cloud computing environment according to an embodiment of the present disclosure.

[0013] FIG. 6 depicts abstraction model layers according to an embodiment of the present disclosure.

DETAILED DESCRIPTION

[0014] The methods, systems, and computer program products of the present disclosure may provide ways to optimize the order fulfillment in an omni-channel retail system.

[0015] Determining optimal order fulfillment in an omni-channel retail system may rely on a diverse set of inputs and considerations. Some inputs that may be used when determining optimal order fulfillment may include, for example, current inventory levels at stores, current inventory levels at distribution centers, how much inventory is currently in transit, the rate at which inventory is being depleted at stores, the rate at which inventory is being depleted at distribution centers, the cost of shipping inventory from distribution centers to stores, the cost of shipping inventory from distribution centers to customer provided delivery addresses, the cost of shipping inventory from stores to customer provided delivery addresses, the cost of shipping inventory from stores to other stores, the cost of markdowns due to unsold inventory, customer loyalty, and other similar criteria.

[0016] FIG. 1 illustrates a schematic of an example computer or processing system 100 that may implement an order fulfillment optimizing system in one embodiment of the present disclosure. The computer system is only one example of a suitable processing system and is not intended to suggest any limitation as to the scope of use or functionality of embodiments of the methodology described herein. The processing system shown may be operational with numerous other general purpose or special purpose computing system environments or configurations. Examples of well-known computing systems, environments, and/or configurations that may be suitable for use with the processing system shown in FIG. 1 may include, but are not limited to, personal computer systems, server computer systems, thin clients, thick clients, handheld or laptop devices, multiprocessor systems, microprocessor-based systems, set top boxes, programmable consumer electronics, network PCs, minicomputer systems, mainframe computer systems, and distributed cloud computing environments that include any of the above systems or devices, and the like.

[0017] The computer system 100 may be described in the general context of computer system executable instructions, such as program modules, being executed by a computer system. Generally, program modules may include routines, programs, objects, components, logic, data structures, and so on that perform particular tasks or implement particular abstract data types. The computer system may be practiced in distributed cloud computing environments where tasks are performed by remote processing devices that are linked through a communications network. In a distributed cloud computing environment, program modules may be located in both local and remote computer system storage media including memory storage devices.

[0018] The components of computer system 100 may include, but are not limited to, one or more processors or processing units 112, a system memory 116, and a bus 114 that couples various system components including system memory 116 to processor 112. The processor 112 may include one or more program modules 110 that perform the methods described herein. The program modules 110 may be programmed into the integrated circuits of the processor 112, or loaded from memory 116, storage device 118, or network 124 or combinations thereof.

[0019] Bus 114 may represent one or more of any of several types of bus structures, including a memory bus or memory controller, a peripheral bus, an accelerated graphics port, and a processor or local bus using any of a variety of bus architectures. By way of example, and not limitation, such architectures include Industry Standard Architecture (ISA) bus, Micro Channel Architecture (MCA) bus, Enhanced ISA (EISA) bus, Video Electronics Standards Association (VESA) local bus, and Peripheral Component Interconnects (PCI) bus.

[0020] Computer system 100 may include a variety of computer system readable media. Such media may be any available media that is accessible by computer system, and it may include both volatile and non-volatile media, removable and non-removable media.

[0021] System memory 116 can include computer system readable media in the form of volatile memory, such as random access memory (RAM) and/or cache memory or others. Computer system 100 may further include other removable/non-removable, volatile/non-volatile computer system storage media. By way of example only, storage system 118 can be provided for reading from and writing to a non-removable, non-volatile magnetic media (e.g., a "hard drive"). Although not shown, a magnetic disk drive for reading from and writing to a removable, non-volatile magnetic disk (e.g., a "floppy disk"), and an optical disk drive for reading from or writing to a removable, non-volatile optical disk such as a CD-ROM, DVD-ROM or other optical media can be provided. In such instances, each can be connected to bus 114 by one or more data media interfaces.

[0022] Computer system 100 may also communicate with one or more external devices 126 such as a keyboard, a pointing device, a display 128, etc.; one or more devices that enable a user to interact with computer system 100; and/or any devices (e.g., network card, modem, etc.) that enable computer system to communicate with one or more other computing devices. Such communication can occur via Input/Output (I/O) interfaces 120.

[0023] Still yet, computer system 100 can communicate with one or more networks 124 such as a local area network (LAN), a general wide area network (WAN), and/or a public network (e.g., the Internet) via network adapter 122. As depicted, network adapter 122 communicates with the other components of computer system via bus 114. It should be understood that although not shown, other hardware and/or software components could be used in conjunction with computer system 100. Examples include, but are not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data archival storage systems, etc.

[0024] With reference to FIG. 2, an optimization model 200 is disclosed. As illustrated in FIG. 2, one or more dimension 210 may be used as inputs into a multi criteria decision analysis framework (MCDA) 220. Dimensions 210 may be, for example, objectives that a user may wish to target as a basis for a final solution. In some embodiments, a dimension 210 may be, for example, optimizing sourcing of items from fulfillment nodes (e.g., stores, distribution centers, etc.) so that the customer receives the order on time and the least expensive shipment option is chosen (Ship from the closest store). In some embodiments, a dimension 210 may be, for example, incentivizing stores that have more inventory and decentivizing stores that have less inventory (Balancing inventory). In some embodiments, a dimension 210 may be, for example, incentivizing stores that have less workload and decentivizing stores that have more workload (Balancing store utilization). In some embodiments, a dimension 210 may be, for example, incentivizing stores that have the risk of having unsold items at the end of the season (Avoiding markdowns). In some embodiments, a dimension 210 may be, for example, delivering orders earlier to customers having more loyalty points (Honoring customer loyalty). In some embodiments, a dimension 210 may be, for example, minimizing the total cost to serve, which may include, for example, improving fulfillment efficiency and speed, improving inventory performance, reducing fulfillment cost, improving customer satisfaction, and improving processing of e-com inventory returned to stores, each of which may also be separate dimensions 210. Some additional dimensions 210 may include, for example, reducing shipping costs, reducing underutilization of fulfillment capacity at a node (stores, e-fulfillment centers (EFCs), distribution centers (DCs), etc.), reducing operational costs including expenses to clear backlogs or to expedite backlogs, increasing inventory utilization savings including money saved by targeting stock keeping unit (SKU)-node pairs identified by markdown lists and money saved by reducing the risk of markdowns and reducing the risk of lost store sales, reducing the cost of cancellation, reducing the load variance costs (impact of deviating from a fulfillment plan at a given node), increasing customer satisfaction savings (projected gain in market share due to improving customer satisfaction by, for example, reducing delivery times), and reducing real-estate costs (difference in cost of real-estate between warehouse and retail store space). Although examples of dimensions 210 have been provided, any other dimensions 210 may be used depending on the particular retail business involved.

[0025] In an embodiment, MCDA 220 is a mathematical model that is configured to address all of the dimensions 210 to provide an optimized output taking each dimension 210 into account. MCDA 220 implements the following formulas to generate an optimized result:

min u , y , w i .di-elect cons. I h .lamda. 1 C ih j y ih + k .di-elect cons. K i .di-elect cons. I .lamda. 2 C ik u ik + k .di-elect cons. K i .di-elect cons. I .lamda. 3 C ik u ik + + k .di-elect cons. K i .di-elect cons. I .lamda. n C ik u ik ##EQU00001## s . t . i .di-elect cons. I ( k ) u ik = min { i .di-elect cons. I ( k ) U ik , Q k } .A-inverted. k .di-elect cons. K ##EQU00001.2## u ik .ltoreq. min { X ik , Q k } .A-inverted. k .di-elect cons. I , i .di-elect cons. I ( k ) ##EQU00001.3## k .di-elect cons. K W k u ik = w i .A-inverted. i .di-elect cons. I ##EQU00001.4## h = 0 H y ih = 1 .A-inverted. i .di-elect cons. I ##EQU00001.5## w i .ltoreq. hy ih .omega. .A-inverted. h = 0 , , H ##EQU00001.6## u ik .di-elect cons. + ; y ih .di-elect cons. { 0 , 1 } , w i .gtoreq. 0. ##EQU00001.7##

[0026] The terms in the above formulas may be defined as follows:

[0027] k.epsilon. denotes a set of SKUs, also called items or units. Each SKU k corresponds to a particular item that may be sold, for example, a blue t-shirt in a large size may have a first SKU k, the same blue t-shirt in a medium size may have a second SKU k, a green t-shirt of the same style in a large size may have a third SKU k, etc. The set of SKUs k may be defined, for example, by the retailer, manufacturer, or any other party.

[0028] i.epsilon.I denotes a set of order fulfillment nodes, for example, stores, EFCs, distribution centers (DCs), warehouses, or any other source having an inventory of SKUs k that can be used for fulfilling orders.

[0029] i.epsilon.I(k) denotes the subset of nodes i from which a specific SKU k can be sourced.

[0030] h.epsilon.1 . . . H denotes the shipping cost for a package of weight class h. The shipping cost is a function of shipping node i, but the shipping node i can be suppressed since index h is always used with index i.

[0031] w.sub.k denotes the weight of an item of SKU k.

[0032] .omega. denotes the width of the weight interval to which total weight of an order from node i belongs. .omega. is related to how shipping costs are calculated by carriers. Different shipping costs may be associated with each weight interval, for example, a first cost for the weight interval [0 pounds, 1 pound], a second cost for the weight interval [1 pound, 2 pounds], etc. In this example, the width co is 1 pound. In another example, there may be a first cost for the weight interval [0 pounds, 2 pounds], and a second cost for the weight interval [2 pounds, 4 pounds], etc. In this example, the width .omega. is 2 pounds.

[0033] c.sub.ih.sup.j denotes the shipping cost to a zip or zone code j from a node i for a package of weight class h.

[0034] X.sub.ik denotes the current available inventory of the item SKU k in node i.

[0035] C.sub.ik denotes the cost of sourcing an item of SKU k from node i.

[0036] Q.sub.k denotes the number of items of SKU k that have been demanded. For example, the number of items of SKU k that have been ordered by customers, the inventory shortfall at a particular store, or any other type of demand.

[0037] .lamda..sub.1 . . . .lamda..sub.n denote multipliers .lamda. for each dimension. In some embodiments multipliers .lamda. may, for example, be a percentage from 0% to 100%. In some embodiments, a decimal representation, e.g., 0.00 to 1.00, may be used. Multipliers .lamda. may denote a weighting that each dimension contributes to the final solution. In some embodiments, multipliers .lamda. may be pre-determined in advance, for example, by a user, by system 10, by a retailer, or in any other manner. In some embodiments, a user of system 100 may be provided with a user interface 300 that allows the user to set values for each multiplier .lamda. as shown, for example, in FIG. 3. User interface 300 may, for example, be displayed on display 128. With reference now to FIG. 3, each dimension 310 includes a corresponding element 320 that is adjustable by the user to set the multiplier .lamda. for the dimension 310. For example, a dimension 312 of reducing backlog includes a slider 322 that is adjustable to set a multiplier .lamda..sub.1, for example, to a value of 25% or 0.25. Accordingly, the multiplier .lamda..sub.1 corresponding to the dimension 312 of reducing backlog is set to 0.25 or 25% using element 322. As further shown in the example provided by FIG. 3, dimensions 314 (Avoid markdown), 316 (Minimize shipping cost), and 318 (Minimize labor cost) may each have corresponding elements 324, 326, and 328 that, in this example, respectively set the corresponding multipliers .lamda..sub.2, .lamda..sub.3 and .lamda..sub.4 to 50% (0.50), 25% (0.25), and 0% (0.00). Although illustrated as sliding elements 320 in FIG. 3, elements 320 may be any other form of input that allows a user to set a value for multipliers .lamda.. For example, alternatively or in addition to sliding elements, a user may enter a value for each multiplier .lamda. directly, e.g., by selecting a multiplier .lamda. and inputting a desired value using a user input device, or may adjust or set the value of multipliers .lamda. in any other similar manner. In some embodiments, multipliers .lamda. may be adjusted automatically by system 100.

[0038] u.sub.ik denotes a decision on whether or not to source units of SKU k from node i. For example, in some embodiments, u.sub.ik may be the number of units of SKU k that have shipped or will be shipped from node i.

[0039] w.sub.i denotes the weight of a package shipped from node i. In some embodiments, the package may include only items of a specific SKU k. In some embodiments, the package may include any items being shipped from node i, regardless of SKU.

[0040] y.sub.ih denotes a binary variable indicating whether or not a package has shipped from node i in weight class h.

[0041] MCDA 220 optimizes the result by solving for both u and y variables simultaneously. In this manner, MCDA 220 brings together multiple dimensions at the same time to find a middle ground between all of the dimensions. In an example, if one dimension is the cost of shipping and another dimension is markdown avoidance, MCDA 220 finds a balance between shipping costs and the cost of future markdowns for the item. For example, MCDA 220 may provide an optimized result based on the fact that 1 dollar in shipping costs now may be offset by the opportunity cost of not sourcing the item effectively which leads to future markdowns and losing that same dollar or more further downstream. In a similar manner MCDA 220 may balance each dimension at the same time to generate the most optimal result.

[0042] In some embodiments, MCDA 220 may be optimized according to one or more models 230 that may provide a basis for a solution. For example, MCDA 220 may be optimized according to a goal programming model 232 to achieve solutions based on goals or target values to be achieved, may be run to achieve pareto optimality 234 such that it is impossible to make one dimension better off without making at least one other dimension worse off, may be run based on constrained service levels 236, or may be run based on any other similar model. As each goal or dimension is added, however, the solution time may increase exponentially such that, for example, obtaining a pareto optimal solution graph, or other outputs from each model 230 may be exponentially more time consuming for each individual problem.

[0043] In some embodiments, a decomposition and heuristic based optimization 240 may be implemented to reduce the solution time and to allow the solution to be generated in or near real-time. Optimization 240 may include the implementation of a sequential approach by solving MCDA 220 for each dimension 210 disjointly using historical data to create a baseline of what a target and service level can or should look like. For example, historical data may be provided by or received from a retailer, e.g., from a database or other storage system via a wired or wireless connection, the internet, or any other communication system, and used as inputs for MCDA 220. The output solutions for each dimension may then be analyzed to determine the right mix of dimension multipliers. In some embodiments, expert opinions may be solicited to assist in optimizing the dimensions multipliers, for example, through the use of user interface 300.

[0044] In an example sequential approach, each dimension 210 or group of dimensions 210 may be solved separately in MCDA 220 and later combined to form an order fulfillment solution. Assuming a minimum solution value for a dimension d is .alpha..sub.d and a maximum value for dimension d is .beta..sub.d. For example in shipping cost minimization, .alpha..sub.d represents minimum shipping cost, and .beta..sub.d represents maximum shipping cost. Sometimes obtaining minimum and maximum values optimally may take considerable time. In that case, heuristic procedures available in commercial optimization solvers can be used. The heuristic procedure used to solve each dimension may differ depending on the type of dimension being solved. Some non-limiting examples of commercial solvers having heuristic methods may include, for example, the Cplex.RTM. solver, the Gurobi.TM. solver, or any other similar solver.

[0045] An iterative process may be used to combine the individual solutions and resolve them to ultimately end up with a global solution to the overall approach. By solving each dimension 210 separately and implementing heuristic procedures, the amount of time required for calculating the solution may be reduced.

[0046] In some embodiments, t.sub.d.epsilon.[.alpha..sub.d, .beta..sub.d] may be used to denote a target value t.sub.d for dimension d assuming a goal of minimizing objective values in each dimension. Target value t.sub.d can be obtained either by user preference or as some percentage value of .alpha..sub.d. For example, t.sub.d may be determined according to the equation t.sub.d=(1+10%)*.alpha..sub.d which indicates that the user is willing to sacrifice 10% optimality from dimension d. For example, where a user desires to achieve a full minimum value, .alpha..sub.d may be used. When the user wishes to sacrifice some optimality of a dimension in favor of other dimensions, the target value t.sub.d may be used in place of .alpha..sub.d.

[0047] For example, the overall problem may be initially solved with a dimensional multiplier .lamda..sub.d of each dimension d having an initial value of 1. The solution Z.sub.d of each individual dimension d may be compared to the minimum value .alpha..sub.d (or target value t.sub.d) and maximum value .beta..sub.d for that dimension d. Depending on where Z.sub.d resides in the interval [.alpha..sub.d, .beta..sub.d] (or [t.sub.d, .beta..sub.d]) the dimensional multiplier .lamda..sub.d may be adjusted, for example, increased or decreased, and the dimension d may solved again using the adjusted .lamda..sub.d multiplier. This process may be performed iteratively such that the value of the dimensional multiplier .lamda..sub.d of each dimension is adjusted until the solution Z.sub.d for each dimension d achieves a desired value in the interval [.alpha..sub.d, .beta..sub.d] (or [t.sub.d, .beta..sub.d]).

[0048] In some embodiments, the iterative process may be performed automatically. For example, system 100 may calculate a satisfaction value, s.sub.d, for each dimension d as s.sub.d=(Z.sub.d-t.sub.d)/(.beta..sub.d-t.sub.d). For example, lower s.sub.d values represent better target achievement for a dimension d while higher s.sub.d values represent worse target achievement for a dimension d. In some embodiments, system 100 may sort the s.sub.d values of each dimension d in increasing order and obtain (d), where (d) denotes the position of a dimension din the sorted sequence. In some embodiments, system 100 may sort s.sub.d values in decreasing order and obtain [d], where [d] denotes the position of a dimension d in the sorted sequence. System 100 may automatically process updates to the multipliers as .lamda..sub.(d)=s.sub.[d]*.lamda..sub.(d) and resolve the overall problem with the updated multipliers. The automatic process may continue by recalculating s.sub.d values for each dimension d, sorting them in ascending and descending order to generate (d) and [d], and resolving the problem until the satisfaction values s.sub.d satisfy pre-determined criteria. In some embodiments, the pre-determined criteria for satisfaction value s.sub.d may be set by a user of system 100. In some embodiments, an iteration of satisfaction value s.sub.d for a dimension d will decrease if the satisfaction value s.sub.d of the previous iteration was greater than the satisfaction values s.sub.d for other dimensions d. In some embodiments, the iteration of satisfaction value s.sub.d for the dimension d will increase if the satisfaction value s.sub.d of the previous iteration was less than the satisfaction values s.sub.d for other dimensions d.

[0049] FIG. 4 illustrates a flow chart implementing optimization 240. At 402, historical data is received from the retailer. At 404, the multiplier .lamda. for each dimension 210 is initially set to 1. In some embodiments multiplier .lamda. for each dimension 210 may alternatively be initially set to any other pre-determined value. For example, a user of system 100 may set the pre-determined value. In some embodiments, each multiplier .lamda. may be set to the same value. In some embodiments, one or more multiplier .lamda. may be set to different values. At 406, each dimension is solved separately based on the respective dimensional multiplier .lamda. and the received historical data to generate an output Z.sub.d for each dimension. At 408, the output Z.sub.d for each dimension 210 is compared to the respective interval [.alpha..sub.d, .beta..sub.d] (or [t.sub.d, .beta..sub.d]) for each dimension 210. In some embodiments, t.sub.d may be set by a user as described above. At 410, system 100 determines whether the dimension multiplier .lamda. for any of dimensions 210 needs to be adjusted based on the comparison from 408. For example, in some embodiments, a user or an expert may review the Z.sub.d and the interval [.alpha..sub.d, .beta..sub.d] (or [t.sub.d, .beta..sub.d]) for a dimension to determine whether an adjustment needs to be made to that dimension. In some embodiments, system 100 may define one or more pre-determined or user set thresholds in the interval [.alpha..sub.d, .beta..sub.d] (or [t.sub.d, .beta..sub.d]) for each dimension. Depending on the relation of Z.sub.d to one or more of the pre-defined thresholds, an adjustment of the dimensional multiplier .lamda. for a particular dimension 210 may be necessary. As an example, if .alpha..sub.d (or t.sub.d) has a value of 5 and .beta..sub.d has a value of 15, system 100 may include thresholds at values of 7, 10, and 12. Depending on the dimension, if the solution Z.sub.d is greater than, less than, or equal to a particular threshold, an adjustment may be necessary. In some embodiments, an adjustment may be required based on what percentage of the interval Z.sub.d is at. For example, a target solution may be at 50% of the interval [.alpha..sub.d, .beta..sub.d] (or [t.sub.d, .beta..sub.d]) where a % higher or lower, say 20% or 70% may require an adjustment.

[0050] At 412, dimensional multipliers .lamda. that are determined to require an adjustment may be adjusted. In some embodiments, adjustments to dimensional multipliers .lamda. may be performed manually by a user or expert, for example, via user interface 300. In some embodiments, adjustments to dimensional multipliers .lamda. may be performed automatically by system 100. In some embodiments, a dimensional multiplier .lamda. may be adjusted by an amount that is based on how far a solution Z.sub.d produced by MCDA 220 based on the dimensional multiplier .lamda. is from a target solution Z.sub.d for the dimension 210. For example, if the interval is [0,100] for the dimension 210 and the target solution Z.sub.d for the dimension 210 is 50, a Z.sub.d between 20 and 30 may require a first adjustment, a Z.sub.d between 30 and 40 may require a second adjustment, and a Z.sub.d between 45 and 55 may require no adjustment. In some embodiments, for example, the first adjustment may be larger than the second adjustment, smaller than the second adjustment, or equal to the second adjustment. As an example, the initial value of 1 for a dimensional multiplier .lamda. may be decreased based on the comparison in 408. For example, a dimensional multiplier .lamda. for a particular dimension 210 may be reduced from 1 to 0.75. Other amounts of reduction or adjustment of a dimensional multiplier .lamda. are also contemplated.

[0051] If an adjustment was necessary at 412, any dimensions of MCDA 220 that have adjusted dimensional multipliers .lamda. may solved to generate updated solutions Z.sub.d at 406, the updated solutions Z.sub.d for each dimension 210 may again be compared to the respective interval [.alpha..sub.d, .beta..sub.d] for each dimension 210 at 408, and a determination may be made at 410 of whether another adjustment is necessary. This process from 406-412 occurs iteratively until the dimensional multipliers .lamda. no longer need to be adjusted by system 100. The multipliers .lamda. may now be considered optimized multipliers .lamda.. In some embodiments, the process from 406-412 may be performed automatically by system 100 without further user input to generate the optimized multipliers .lamda..

[0052] Once multipliers .lamda. have been optimized, current data may be received at 414. Current data may be data relating to current inventory and stock levels of various SKUs, current customer demand levels for the SKUs, or any other current data related to the current state of the retailers business. At 416, each dimension of MCDA 220 may be solved based on the current data and the optimized multipliers .lamda. for each dimension. The solutions Z.sub.d for each dimension may then be combined according to MCDA 220 to generate a combined solution Z.sub.o as an output to MCDA 220. At 418 the solved values of the combined solution Z.sub.o may be implemented by the retailer's order fulfillment system and the order fulfillment system may perform order fulfillment based on the combined solution Z.sub.o.

[0053] As will be appreciated by one skilled in the art, aspects of the present invention may be embodied as a system, method or computer program product. Accordingly, aspects of the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment (including firmware, resident software, micro-code, etc.) or an embodiment combining software and hardware aspects that may all generally be referred to herein as a "circuit," "module" or "system." Furthermore, aspects of the present invention may take the form of a computer program product embodied in one or more computer readable medium(s) having computer readable program code embodied thereon.

[0054] Any combination of one or more computer readable medium(s) may be utilized. The computer readable medium may be a computer readable signal medium or a computer readable storage medium. A computer readable storage medium may be, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any suitable combination of the foregoing. More specific examples (a non-exhaustive list) of the computer readable storage medium would include the following: a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing. In the context of this document, a computer readable storage medium may be any tangible medium that can contain, or store a program for use by or in connection with an instruction execution system, apparatus, or device.

[0055] A computer readable signal medium may include a propagated data signal with computer readable program code embodied therein, for example, in baseband or as part of a carrier wave. Such a propagated signal may take any of a variety of forms, including, but not limited to, electro-magnetic, optical, or any suitable combination thereof. A computer readable signal medium may be any computer readable medium that is not a computer readable storage medium and that can communicate, propagate, or transport a program for use by or in connection with an instruction execution system, apparatus, or device.

[0056] Program code embodied on a computer readable medium may be transmitted using any appropriate medium, including but not limited to wireless, wireline, optical fiber cable, RF, etc., or any suitable combination of the foregoing.

[0057] Computer program code for carrying out operations for aspects of the present invention may be written in any combination of one or more programming languages, including an object oriented programming language such as Java, Smalltalk, C++ or the like and conventional procedural programming languages, such as the "C" programming language or similar programming languages, a scripting language such as Perl, VBS or similar languages, and/or functional languages such as Lisp and ML and logic-oriented languages such as Prolog. The program code may execute entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer or entirely on the remote computer or server. In the latter scenario, the remote computer may be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection may be made to an external computer (for example, through the Internet using an Internet Service Provider).

[0058] Aspects of the present invention are described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and/or block diagrams, and combinations of blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions/acts specified in the flowchart and/or block diagram block or blocks.

[0059] These computer program instructions may also be stored in a computer readable medium that can direct a computer, other programmable data processing apparatus, or other devices to function in a particular manner, such that the instructions stored in the computer readable medium produce an article of manufacture including instructions which implement the function/act specified in the flowchart and/or block diagram block or blocks.

[0060] The computer program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other devices to cause a series of operational steps to be performed on the computer, other programmable apparatus or other devices to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide processes for implementing the functions/acts specified in the flowchart and/or block diagram block or blocks.

[0061] The flowchart and block diagrams in the figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods and computer program products according to various embodiments of the present invention. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of code, which comprises one or more executable instructions for implementing the specified logical function(s). It should also be noted that, in some alternative implementations, the functions noted in the block may occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and/or flowchart illustration, and combinations of blocks in the block diagrams and/or flowchart illustration, can be implemented by special purpose hardware-based systems that perform the specified functions or acts, or combinations of special purpose hardware and computer instructions.

[0062] The computer program product may comprise all the respective features enabling the implementation of the methodology described herein, and which--when loaded in a computer system--is able to carry out the methods. Computer program, software program, program, or software, in the present context means any expression, in any language, code or notation, of a set of instructions intended to cause a system having an information processing capability to perform a particular function either directly or after either or both of the following: (a) conversion to another language, code or notation; and/or (b) reproduction in a different material form.

[0063] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms "comprises" and/or "comprising," when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof.

[0064] The corresponding structures, materials, acts, and equivalents of all means or step plus function elements, if any, in the claims below are intended to include any structure, material, or act for performing the function in combination with other claimed elements as specifically claimed. The description of the present invention has been presented for purposes of illustration and description, but is not intended to be exhaustive or limited to the invention in the form disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the invention. The embodiment was chosen and described in order to best explain the principles of the invention and the practical application, and to enable others of ordinary skill in the art to understand the invention for various embodiments with various modifications as are suited to the particular use contemplated.

[0065] Various aspects of the present disclosure may be embodied as a program, software, or computer instructions embodied in a computer or machine usable or readable medium, which causes the computer or machine to perform the steps of the method when executed on the computer, processor, and/or machine. A program storage device readable by a machine, tangibly embodying a program of instructions executable by the machine to perform various functionalities and methods described in the present disclosure is also provided.

[0066] The system and method of the present disclosure may be implemented and run on a general-purpose computer or special-purpose computer system. The terms "computer system" and "computer network" as may be used in the present application may include a variety of combinations of fixed and/or portable computer hardware, software, peripherals, and storage devices. The computer system may include a plurality of individual components that are networked or otherwise linked to perform collaboratively, or may include one or more stand-alone components. The hardware and software components of the computer system of the present application may include and may be included within fixed and portable devices such as desktop, laptop, and/or server. A module may be a component of a device, software, program, or system that implements some "functionality", which can be embodied as software, hardware, firmware, electronic circuitry, or etc.

[0067] It is to be understood that although this disclosure includes a detailed description on cloud computing, implementation of the teachings recited herein are not limited to a cloud computing environment. Rather, embodiments of the present invention are capable of being implemented in conjunction with any other type of computing environment now known or later developed.

[0068] Cloud computing is a model of service delivery for enabling convenient, on-demand network access to a shared pool of configurable computing resources (e.g., networks, network bandwidth, servers, processing, memory, storage, applications, virtual machines, and services) that can be rapidly provisioned and released with minimal management effort or interaction with a provider of the service. This cloud model may include at least five characteristics, at least three service models, and at least four deployment models.

[0069] Characteristics are as Follows:

[0070] On-demand self-service: a cloud consumer can unilaterally provision computing capabilities, such as server time and network storage, as needed automatically without requiring human interaction with the service's provider.

[0071] Broad network access: capabilities are available over a network and accessed through standard mechanisms that promote use by heterogeneous thin or thick client platforms (e.g., mobile phones, laptops, and PDAs).

[0072] Resource pooling: the provider's computing resources are pooled to serve multiple consumers using a multi-tenant model, with different physical and virtual resources dynamically assigned and reassigned according to demand. There is a sense of location independence in that the consumer generally has no control or knowledge over the exact location of the provided resources but may be able to specify location at a higher level of abstraction (e.g., country, state, or datacenter).

[0073] Rapid elasticity: capabilities can be rapidly and elastically provisioned, in some cases automatically, to quickly scale out and rapidly released to quickly scale in. To the consumer, the capabilities available for provisioning often appear to be unlimited and can be purchased in any quantity at any time.

[0074] Measured service: cloud systems automatically control and optimize resource use by leveraging a metering capability at some level of abstraction appropriate to the type of service (e.g., storage, processing, bandwidth, and active user accounts). Resource usage can be monitored, controlled, and reported, providing transparency for both the provider and consumer of the utilized service.

[0075] Service Models are as Follows:

[0076] Software as a Service (SaaS): the capability provided to the consumer is to use the provider's applications running on a cloud infrastructure. The applications are accessible from various client devices through a thin client interface such as a web browser (e.g., web-based e-mail). The consumer does not manage or control the underlying cloud infrastructure including network, servers, operating systems, storage, or even individual application capabilities, with the possible exception of limited user-specific application configuration settings.

[0077] Platform as a Service (PaaS): the capability provided to the consumer is to deploy onto the cloud infrastructure consumer-created or acquired applications created using programming languages and tools supported by the provider. The consumer does not manage or control the underlying cloud infrastructure including networks, servers, operating systems, or storage, but has control over the deployed applications and possibly application hosting environment configurations.

[0078] Infrastructure as a Service (IaaS): the capability provided to the consumer is to provision processing, storage, networks, and other fundamental computing resources where the consumer is able to deploy and run arbitrary software, which can include operating systems and applications. The consumer does not manage or control the underlying cloud infrastructure but has control over operating systems, storage, deployed applications, and possibly limited control of select networking components (e.g., host firewalls).

[0079] Deployment Models are as Follows:

[0080] Private cloud: the cloud infrastructure is operated solely for an organization. It may be managed by the organization or a third party and may exist on-premises or off-premises.

[0081] Community cloud: the cloud infrastructure is shared by several organizations and supports a specific community that has shared concerns (e.g., mission, security requirements, policy, and compliance considerations). It may be managed by the organizations or a third party and may exist on-premises or off-premises.

[0082] Public cloud: the cloud infrastructure is made available to the general public or a large industry group and is owned by an organization selling cloud services.

[0083] Hybrid cloud: the cloud infrastructure is a composition of two or more clouds (private, community, or public) that remain unique entities but are bound together by standardized or proprietary technology that enables data and application portability (e.g., cloud bursting for load-balancing between clouds).

[0084] A cloud computing environment is service oriented with a focus on statelessness, low coupling, modularity, and semantic interoperability. At the heart of cloud computing is an infrastructure that includes a network of interconnected nodes.

[0085] Referring now to FIG. 1, illustrative cloud computing environment 50 is depicted. As shown, cloud computing environment 50 includes one or more cloud computing nodes 10 with which local computing devices used by cloud consumers, such as, for example, personal digital assistant (PDA) or cellular telephone 54A, desktop computer 54B, laptop computer 54C, and/or automobile computer system 54N may communicate. Nodes 10 may communicate with one another. They may be grouped (not shown) physically or virtually, in one or more networks, such as Private, Community, Public, or Hybrid clouds as described hereinabove, or a combination thereof. This allows cloud computing environment 50 to offer infrastructure, platforms and/or software as services for which a cloud consumer does not need to maintain resources on a local computing device. It is understood that the types of computing devices 54A-N shown in FIG. 1 are intended to be illustrative only and that computing nodes 10 and cloud computing environment 50 can communicate with any type of computerized device over any type of network and/or network addressable connection (e.g., using a web browser).

[0086] Referring now to FIG. 2, a set of functional abstraction layers provided by cloud computing environment 50 (FIG. 1) is shown. It should be understood in advance that the components, layers, and functions shown in FIG. 2 are intended to be illustrative only and embodiments of the invention are not limited thereto. As depicted, the following layers and corresponding functions are provided:

[0087] Hardware and software layer 60 includes hardware and software components. Examples of hardware components include: mainframes 61; RISC (Reduced Instruction Set Computer) architecture based servers 62; servers 63; blade servers 64; storage devices 65; and networks and networking components 66. In some embodiments, software components include network application server software 67 and database software 68.

[0088] Virtualization layer 70 provides an abstraction layer from which the following examples of virtual entities may be provided: virtual servers 71; virtual storage 72; virtual networks 73, including virtual private networks; virtual applications and operating systems 74; and virtual clients 75.

[0089] In one example, management layer 80 may provide the functions described below. Resource provisioning 81 provides dynamic procurement of computing resources and other resources that are utilized to perform tasks within the cloud computing environment. Metering and Pricing 82 provide cost tracking as resources are utilized within the cloud computing environment, and billing or invoicing for consumption of these resources. In one example, these resources may include application software licenses. Security provides identity verification for cloud consumers and tasks, as well as protection for data and other resources. User portal 83 provides access to the cloud computing environment for consumers and system administrators. Service level management 84 provides cloud computing resource allocation and management such that required service levels are met. Service Level Agreement (SLA) planning and fulfillment 85 provide pre-arrangement for, and procurement of, cloud computing resources for which a future requirement is anticipated in accordance with an SLA.

[0090] Workloads layer 90 provides examples of functionality for which the cloud computing environment may be utilized. Examples of workloads and functions which may be provided from this layer include: mapping and navigation 91; software development and lifecycle management 92; virtual classroom education delivery 93; data analytics processing 94; transaction processing 95; and omni-channel order fulfillment optimization 96.

[0091] The embodiments described above are illustrative examples and it should not be construed that the present invention is limited to these particular embodiments. Thus, various changes and modifications may be effected by one skilled in the art without departing from the spirit or scope of the invention as defined in the appended claims.

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